Answer:
9.9 feet.
Step-by-step explanation:
Solution:
- If the swing were to hang straight down, it would be hanging at an angle of -90 degrees from the horizontal. If it is moving from -45 degrees from the horizontal to -135 degrees from the horizontal, this means that it is swinging from 45 degrees to the right of the straight-down position to 45 degrees to the left of the straight-down position.
- The swing is of length L = 10 - 3 = 7 feet. Recall that it hangs from a beam 10 feet above the ground and the seat hangs 3 feet above the ground in its straight-down rest position.
- Let's consider the swing at one of its extreme positions where it makes an angle of 45 degrees from the vertical. In this position, you can imagine the swing forming a right triangle with the highest vertex angle being 45 degrees and the hypotenuse being L = 7 feet. To calculate the horizontal leg of this triangle, you would use the sine function.
sin(45 deg) = x/L
So,
x = L*sin(45 deg)
x = 7*sin(40 deg) = 4.95 feet
- But, this is only the horizontal distance that the swing traverses from one extreme position to hanging straight down. It needs to complete its motion and swing up to the other extreme position. So, in moving from one extreme position to the other, the swing traverses a horizontal distance of
2x = 2*4.95 feet = 9.9 feet.
Answer:
Add 3 to X to get Y
Step-by-step explanation:
1 + 3 = 4
2 + 3 = 5
We have been given a conditional statement and we are asked to find out whether this statement can be written as a bi-conditional statement or not.
First of all we will see what a bi-conditional statement is? A bi-conditional statement is a statement when the statement and its converse both are true. The first part of the statement tells a hypothesis and the last part tells us the conclusion of that hypothesis.
Since we know that 2 is a prime number and its not odd, so our given statement is false.
Now look at the converse of this statement. We can see by counter example of 9 that 9 is an odd number but it is not prime number.
Therefore, option D is the correct choice.
Answer:
Step-by-step explanation:
Equation of circle: (x - h)² + (y -k)² = r²
(x+ 3)² + (y + 9)² = 144
(x+ 3)² + (y + 9)² = 12²
h = -3 ; k = -9
Well, we can set x as the number to represent that number which when added to -37 equals to -19.
-37 + x = -19
Add 37 to each side
x = 18
